At Natural Math, Maria Droujkova facilitates online math courses on a pay-what-you-can model. All Natural Math’s materials are published under a Creative Commons license, and its success relies on the ability to freely access, test, and edit the content. “Every parent needs to tweak it; every teacher needs to tweak it. How do you tweak it if it’s prohibited?” asks Maria.

For Maria, free access goes hand-in-hand with running a sustainable company. In one course, half of the participants joined for free, and Maria’s compensation was still comparable to a traditional university course. “CC licenses are central to every part of our process: for content development, for quality assurance, for translations, for publishing new books, and for crowdfunding.”

According to Dr. Maria Droujkova, anyone can learn calculus, even five-year-old children. How do people respond when she tells them that? She laughs at the question: “How do you think people respond?”

But after the initial shock, Maria’s ideas catch on quickly. Through her company Natural Math, she’s built a network of educators, parents, curriculum developers, and students who are turning math education on its head by rethinking traditional ideas of what concepts children are capable of learning. And by publishing all of its materials for free under a Creative Commons license, Natural Math is proving that free access can go hand-in-hand with running a sustainable company.

But can five-year-olds really learn calculus? “There’s calculus, and then there’s calculus,” Maria jokes. “I don’t think that children should be doing what undergrads in Calculus 101 are doing, and actually I don’t think undergrads should be doing that either. But calculus is a view on the world. You can see how big things are made of small things and even infinitesimal things. Kids play with this idea when they play with LEGO bricks.”

If you download Natural Math’s book Moebius Noodles, you’ll find lots of activities designed to stimulate learning through play. Activities feature toy bricks, crayons, chalk, and yes, even noodles. As Maria said in an interview in The Atlantic, “What is learned without play is qualitatively different. It helps with test taking and mundane exercises, but it does nothing for logical thinking and problem solving.”

Natural Math facilitates online courses on a pay-what-you-can basis. Parents and teachers study and discuss strategies for teaching mathematics concepts, and then test and hone those strategies with the children they work with. Maria explains how everything Natural Math publishes relies upon that continual feedback from participants: “It starts with a community incubator, and then we do beta testing online with a lot of parents and teachers, and then we do revisions as a group of authors, and we publish under Creative Commons licenses.”

That’s why the pay-what-you-can model is so important to Natural Math’s process. The materials are only successful because parents and teachers have tested them, and some of those parents and teachers wouldn’t be able to participate if they had to pay. Maria has worked with parents and educators in Iran, who can’t pay a US company because of trade restrictions. And even in North America, some people simply can’t afford it. “We get a lot of letters from US people saying, ‘I am a teacher with a $0 budget for materials.’ You don’t have to go across the ocean to find that need.”

Maria gives the example of a recent course on multiplication. The suggested cost was 20 dollars, but about half of the participants joined for free. And the other half? “They told us it’s too low,” she laughs. She explains that her total compensation from the course was comparable to what adjunct professors make. And, she’s quick to point out, “We don’t have university overhead. There are no intermediaries.”

For Maria, providing materials and courses at no cost is just one side of the coin. For materials to be truly free, users must be able to edit and reuse them. “You need to be able to tweak it, to localize it. Every parent needs to tweak it; every teacher needs to tweak it. How do you tweak it if it’s prohibited? And having tweaked it and remixed it, you need to share it with other people who are in a similar position.” Thanks to the permissions granted by Creative Commons licenses, educators on every continent have translated and edited Natural Math materials and incorporated them into their classwork.

Maria believes that Creative Commons licenses have the power to transform the textbook industry. “I really would highly recommend it for people who are in a similar position; who are trying to innovate and collaborate and grow something new. CC licenses are central to every part of our process: for content development, for quality assurance, for translations, for publishing new books, and for crowdfunding.”

In classrooms, homes, and informal learning circles around the world, children and adults are learning new ways to examine and understand the world through play. And Maria and her team are learning through play too: by inviting their customers to create and explore with them, they’re redefining what it means to be a publishing company.

The illustration of Maria Droujkova was created by Luke Surl. To the extent possible under the law, Luke Surl has waived all copyright and related or neighboring rights under the CC0 Public Domain Declaration.